hi,

 

what this distance metric is called that equal

∑ ABS(ai-bi)

 

thanks

In the context of just the real numbers this metric is called the absolute difference.

And in the context of R^n it's called the taxicab metric or L1 metric (though I am not 100% certain that the captial letter is an L - but somewhat sure), or -according to the German Wikipedia- Manhattan metric (never heard or used that term myself, though).

 

If you plan on posting more mathematical expressions on sfn in the future (you already have 44 posts here, after all), then I recommend looking into the Latex capabilities of this forum (just search for "latex" on this forum).

And in the context of R^n it's called the taxicab metric or L1 metric (though I am not 100% certain that the captial letter is an L - but somewhat sure), or -according to the German Wikipedia- Manhattan metric (never heard or used that term myself, though).

 

This is not nomencalture I know, but that is also what MathWorld uses. You can also read more at Wikipedia.

I thought that I had read somewhere that using a distance metric that

violated the triangle inequality would cause the kernal matrix not be be pos

def. Perhaps that was just in regards to using the metric "raw" versus

within a kernal (e.g. as the distance within an RBF kernal perhaps?)

Frankly, I just don't understand kernals well enough. I don't understand

what effect a measure that violates the triangle inequality has on the

feature space and I don't understand how such a measure when made into a

proper metric "works" in the feature space.

I don't see how this metric violates the triangle inequality and I particularly do not understand the rest of your post.